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Nonlinear Eigenvalue Equations with Varying Coefficients

In: Homotopy Analysis Method in Nonlinear Differential Equations

Author

Listed:
  • Shijun Liao

    (Shanghai Jiao Tong University)

Abstract

Five different types of examples are used to illustrate the validity of the HAM-based Mathematica package BVPh (version 1.0) for nonlinear eigenvalue equations F in a finite interval 0 ≤z ≤a, subject to the n linear boundary conditions B (1 ≤ k ≤ n), where F denotes a nth-order nonlinear ordinary differential operator, ℐ is a linear differential operator, B is a constant, u(z) and α denote eigenfunction and eigenvalue, respectively. These examples verify that, using the BVPh 1.0, multiple solutions of some highly nonlinear eigenvalue equations with singularity and/or multipoint boundary conditions can be found by means of different initial guesses and different types of base functions.

Suggested Citation

  • Shijun Liao, 2012. "Nonlinear Eigenvalue Equations with Varying Coefficients," Springer Books, in: Homotopy Analysis Method in Nonlinear Differential Equations, chapter 0, pages 315-361, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25132-0_9
    DOI: 10.1007/978-3-642-25132-0_9
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